A demand exists for data transmissions at a rate of 50 gigabits per second (Gbps) or more over distances greater than 10 kilometers (km). Several optical data transmission techniques have been proposed for meeting this demand, but each has drawbacks. 10 gigabit per second on/off keying (10 G OOK) meets the optical dispersion requirement, but the data rate under this technique might be too low. Coherent transmission can provide a high capacity but might be too expensive. 50 Gbps OOK/PAM4 (4-level pulse amplitude modulation) without dispersion pre-compensation might not provide enough dispersion tolerance. 50 Gbps OOK/PAM4 with dispersion pre-compensation might be too expensive and might require an external IQ modulator (where “I” is the “in-phase” component of a waveform, and “Q” represents a quadrature component). A non-coherent system has the advantages of low cost, small footprint and low power consumption but has the drawback of low dispersion tolerance. In a high-speed, long-distance data transmission scenario, one problem is dispersion, wherein spectral side bands of different carrier frequencies destructively interfere with one another. For example, for a 50 Gbps or more transmission, the propagation distance is currently limited to a few kilometers over the most popular non-dispersion shifted single mode fiber (G.652) because of dispersion.